The conclusion falls a bit flat, but Livio’s trip through mathematical history is thoroughly enjoyable and requires no...
Why does math describe reality so well? A scientist offers tentative answers.
Livio (The Equation that Couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry, 2005, etc.), an astrophysicist at the Hubble Space Telescope Science Institute, frames his investigation with a history of math, beginning with the key question: Are mathematical truths discovered or invented? Pythagoras came down firmly on the side of discovery. His argument convinced Plato, and thus almost every ancient philosopher of note. The default assumption throughout most of history was that numbers, geometric figures and other mathematical truths are real. Galileo was the first to argue that scientific truth was necessarily expressed in mathematical terms. Newton’s highly accurate calculations of the gravitational force drove the point home, implying that math and physical reality were two sides of the same coin. Even probability and statistics, which seem fuzzier than the hard equations of physics, give useful answers in the world of quantum interactions. But then math began to explore realms of thought that had no obvious relation to the world as we experience it: non-Euclidean geometry, or the paradoxes of set theory and symbolic logic. The idea that math was a game invented by mathematicians rather than something inherent in reality became fashionable, perhaps even inescapable. Also, it became clear that certain undeniably useful scientific disciplines—Darwinian evolution, to name one salient example—resisted mathematical treatment. Even so, Livio shows that correspondences between mathematical discoveries and physical phenomena continued to crop up, often in abstract mathematics created without any idea of practical applications, such as Einstein’s use of non-Euclidean geometry. Knot topology, devised to explain a long-discredited model of the atom, turned out to have application to string theory. The author gives no final answer to the central question of math’s relationship to reality. There are physical phenomena that are modeled by math, he asserts, but we also understand reality with a brain wired to find mathematical relations all around it.
The conclusion falls a bit flat, but Livio’s trip through mathematical history is thoroughly enjoyable and requires no special training to follow it.Pub Date: Jan. 6, 2009
ISBN: 978-0-7432-9405-8
Page Count: 320
Publisher: Simon & Schuster
Review Posted Online: May 19, 2010
Kirkus Reviews Issue: Nov. 1, 2008
This is not the Nutcracker sweet, as passed on by Tchaikovsky and Marius Petipa. No, this is the original Hoffmann tale of 1816, in which the froth of Christmas revelry occasionally parts to let the dark underside of childhood fantasies and fears peek through. The boundaries between dream and reality fade, just as Godfather Drosselmeier, the Nutcracker's creator, is seen as alternately sinister and jolly. And Italian artist Roberto Innocenti gives an errily realistic air to Marie's dreams, in richly detailed illustrations touched by a mysterious light. A beautiful version of this classic tale, which will captivate adults and children alike. (Nutcracker; $35.00; Oct. 28, 1996; 136 pp.; 0-15-100227-4)
Pub Date: Oct. 28, 1996
ISBN: 0-15-100227-4
Page Count: 136
Publisher: Harcourt
Review Posted Online: May 19, 2010
Kirkus Reviews Issue: Aug. 15, 1996
BOOK REVIEW
BOOK REVIEW
An extravaganza in Bemelmans' inimitable vein, but written almost dead pan, with sly, amusing, sometimes biting undertones, breaking through. For Bemelmans was "the man who came to cocktails". And his hostess was Lady Mendl (Elsie de Wolfe), arbiter of American decorating taste over a generation. Lady Mendl was an incredible person,- self-made in proper American tradition on the one hand, for she had been haunted by the poverty of her childhood, and the years of struggle up from its ugliness,- until she became synonymous with the exotic, exquisite, worshipper at beauty's whrine. Bemelmans draws a portrait in extremes, through apt descriptions, through hilarious anecdote, through surprisingly sympathetic and understanding bits of appreciation. The scene shifts from Hollywood to the home she loved the best in Versailles. One meets in passing a vast roster of famous figures of the international and artistic set. And always one feels Bemelmans, slightly offstage, observing, recording, commenting, illustrated.
Pub Date: Feb. 23, 1955
ISBN: 0670717797
Page Count: -
Publisher: Viking
Review Posted Online: Oct. 25, 2011
Kirkus Reviews Issue: Feb. 1, 1955
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